Maa Brahmcharini is the second form of Maa Durga, in this form she did hard penance(Tapasya) to get Lord Shiva as her Husband.
दधाना करपद्माभ्यामक्षमालाकमण्डलू। देवी प्रसीदतु मयि ब्रह्मचारिण्यनुत्तमा॥
On the second day of Navratri, the worship of Mother Brahmacharini is the law of worship.Mother Brahmacharini means that Brahma means austerity and churni, that is to behave.This is made of mother Brahmacharini.
It is said that the goddess of the Himalayas had taken birth and they had made Ghor penance in order to get Lord Shiva in her form. This is the reason why he is called by the name of Brahmacharini due to his hard penance. It is said about the mother that during austerity, the mother spent only one thousand years on eating fruits and vegetables. Not only this, it is also believed that mother has tried many hardships during this time. The mother lived under the open sky and kept fasting for many days, with rain and sunshine.
It is also said that in order to please Lord Shankar, eat Bilvas and worship Bhole Shankar.After some time Bilv Pata Khan, Mother Brahmacharini had auspiciousness and austerity for Lord Shiva without eating anything. It is said that the name of Lord Brahmacharini was also aparna because of leaving the letter to the Bilvas. Due to being dry and fasting and due to the ascetic, the body of Goddess Mother became utterly weakened.
After this the Goddess, the sage was very pleased with the auspices of Mother Brahmacharini and they praised the austerity of the mother. After this, all blessed the mother Brahmacharini and said that Goddess your wish will definitely be fulfilled. The story of Maa Brahmacharini tells us that even after the struggle in life, we should remain firm in our place and should not be left behind by karma.